The Appearance of Matter Fields From Quantum Fluctuations of 2d-Gravity

It is established that various critical regimes may occur for a model of two-dimensional pure quantum gravity. These regimes correspond to the presence of effective fields with scaling dimensions Δ k =−γ str ·k/2, k=1, 2, 3 ..., where γ str =−1/m, m=2, 3, 4 ... is the critical exponent of “string susceptibility” (with respect to the cosmological constant). This behaviour is typical for unitary conformal fields with the central charge c=1−6/m(m+1) in the presence of 2D-quantum gravity. We use the framework of loop equations for the invariant boundary functional, which are exactly solvable in this case.